The invention relates to electron tubes having cold cathodes based on carbon nanotubes, which, compared with other technologies, increase stability, maximum current before electromigration, lifetime and form factor. Carbon nanotubes are formed from carbon having essentially sp2 bonds. They take the form of long thin hollow cylinders often closed at their ends and may be of two varieties: SWNT (single-walled carbon nanotube) and MWNT (multi-walled carbon nanotube). A single-walled nanotube, when it is perfect, may be defined as a graphene sheet (hexagonal carbon lattice) rolled up and closed on itself, thus forming a cylinder of monoatomic thickness consisting only of carbon atoms. What is thus obtained is a tube having a diameter of typically 0.7 to a few nm with a length ranging from a few tens of nanometers to a few millimeters. A multi-walled nanotube is essentially formed from a concentric contiguous stacking of graphene cylinders, for example 7 to 10 cylinders, with for example an inside diameter of a few nanometers and an outside diameter of about 15 nanometers or more.
According to the prior art, an electron tube of this type comprises cathodes based on a uniform arrangement of carbon nanotubes spaced apart by one to two times their height and aligned vertically, perpendicular to the conducting substrate that supports them. These cathodes have already achieved currents of 10 mA over an area of 0.5×0.5 mm2 and beam current densities (over macroscopic areas) of 4 A/cm2 in continuous mode and a peak current density of 15 A/cm2 in 1.5 GHz modulated emission mode. These current densities are lower than those provided by metal-tipped cathodes, but they are close to those emitted by thermionic cathodes, of the order of 1 to 10 A/cm2 at the source, making it possible after concentration to obtain beams having a current density of the order of 50 to 100 A/cm2. It should be noted in this regard that the beams from thermionic cathodes can be concentrated more easily (the cathodes themselves may be given a focusing shape) than the beams emitted by cold cathodes. This requires, in the case of cold cathodes, on the one hand, collimation optics and, on the other hand, a much higher current density at the source.
There is an increasing need for higher current densities in order to be able to provide the market with microwave amplifiers and oscillators that are more compact, lighter and of higher power, electrically or optically controlled THz sources, high-brightness ultraviolet and X-ray sources, and more generally to improve system performance: transmission rate (digital radio or television), brightness (UV or X-ray sources), compactness, etc. There is also an increasing need for these dense beams to be of better quality, notably more monoenergetic, so as to simplify the optics, and collectors (notably in traveling-wave tubes). Moreover, the practical electrical conductivity, electrical cut-off frequency, thermal conductivity and plasma frequency values of nanotubes restrict the effectiveness of their use in certain applications. In particular, they are no longer conducting at optical frequencies, thereby preventing them from being used in direct optical control devices, in particular in generators.
There is therefore a need at the present time for cold-cathode electron tubes that can meet these various criteria, and notably provide electron beams that are more dense (current density of the order of 10 to 100 A/cm2), and more monoenergetic, while still remaining very compact and stable.
Cold cathodes based on nanotubes have in this regard technological limitations that prevent any hope of improving their performance sufficiently. Notably, the moderate conductivity of the material obtained in practice leads to a voltage drop along the nanotube: heat deposition by the Joule effect along the nanotube. This results in a limitation of the currents emitted, so as not to risk destruction of the nanotubes by heat, and consequently a limitation in the current density at the source. This is because above a certain current density, the destruction of the nanotubes is observed.
It may be demonstrated that this destruction occurs when a “destruction” temperature is exceeded.
After destruction of a nanotube, an extended area (an area with a diameter of the order of 10 μm around the initial position of the nanotube) is generally observed in which the silicon substrate is molten (the melting point of silicon Tm(Si): 1687 K).
This may be explained by the thermal dissipation through the Joule effect in the carbon nanotube: when a current I flows through the nanotube, its temperature increases because of this thermal dissipation.
A nanotube may be considered as a one-dimensional conductor. When a current I flows through said nanotube, its temperature increases with the position along the axis and the maximum temperature is reached at its end.
Using the one-dimensional heat equation (taking Joule heating and thermal conduction along the nanotube into consideration and neglecting radiation), it is easy to express the temperature at the tip of the nanotube Ttip as a function of the temperature of the substrate Tsubstrate:Ttip=Tsubstrate+I×Pdissipated/(2κS),where I is the length of the nanotube (in meters), Pdissipated is the power dissipated in the nanotube (in watts), κ is the thermal conductivity of the nanotube (in W·m−1·K−1), and S=πr2 is the cross section of the nanotube (in m2) where r is the radius of the nanotube.
The thermal conductivity of carbon nanotubes has been experimentally determined and various values ranging between κ=25 W·m−1K−1 and κ=200 W·m−1·K−1 are found in the literature.
Taking a nanotube length l=5 μm and a nanotube radius r=25 nm, it is then possible to plot the change in temperature at the tip of the nanotube as a function of the dissipated power, for various values of the thermal conductivity.
The results are shown in FIG. 1 for three values of the thermal conductivity κ: 25, 100 and 200 W·m−1·K−1. It should be noted that the 100 W·m−1·K−1 value of κ seems the most probable one for MWNTs (multi-walled nanotubes).
The graph in FIG. 1 also shows the melting point of carbon Tm(C), which is 4100 K, and the temperature Tdisintegration at which, according to the literature, the tip of the nanotubes subjected to the emission electric field starts to disintegrate, i.e. 2000 K.
This graph shows that the power dissipated (a few tenths of mW) in the usual nanotubes, the resistance of which ranges from the order of a few tens of kilohms to one hundred kilohms, when they emit currents of the order of 0.1 mA, enables very high temperatures to be reached at their tips, or even the disintegration temperature. This therefore results in the destruction of the emitter and the formation of a conduction channel between the cathode and the anode, with formation of an electric arc that causes a crater to be observed.
The aim of the invention is to increase the power of cold-cathode electron tubes and to make them more compact, lighter and more efficient. More particularly with regard to UV and X-ray sources, the aim is also to increase the brightness, so as to improve the resolution thereof and to minimize analysis times. This requires having cold-cathode electron tubes capable of delivering highly monoenergetic electron beams with a high current density.
One idea at the basis of the invention is to reduce the resistance of the nanotube so as, on the one hand, to make the beam more monoenergetic and, on the other hand, to prevent or limit the deposition of heat by the Joule effect along the axis of the nanotube, so as to move back the destruction temperature and thus allow higher current densities.
In the invention, to solve the current density limitation problem in the nanotubes of cold cathodes according to the prior art, one idea is to form an emitter based on a carbon nanotube that is no longer hollow but on the contrary is one such that the inside of the cylinder contains a metallic material.
Metal-cored nanotubes are known in the prior art, for example those having metal cores of Pb, Cu, Fe, Co, Ni, Sn, etc. Such nanotubes have been fabricated and studied, demonstrating that they possess useful magnetic properties enabling magnetic data storage and read devices to be produced, as explained in the article “Enhanced magnetic coercivities in Fe Nanowires” by N. Grobert et al., Applied Physics Letters, Vol. 75, No. 21, Nov. 22, 1999.
Also known, from the application US 2002/0006489 published on Jan. 17, 2002, is an emitter formed from a hydrogenated carbon nanotube, formed by a metal protrusion covered with a hydrogenated carbon nanotube. Such an emitter is designed for applications requiring low currents in a “bad” vacuum environment. Here, the metal structure enables the conductance to be maintained if the perimeter of the emitter becomes damaged due to the electron bombardment that occurs in such an environment.
The invention relates to emitters capable of providing very high current densities, of the order of 10 to 100 amps/cm2, whereas in the aforementioned document there were low current densities of the order of 10 milliamps/cm2.